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202                      ANALYTICAL MECHANICS
12.   Find the power lost due to friction in the bearings of a water turbine under the following conditions:
The rotating system, which weighs 50 tons, is supported by a
flat-end pivot bearing 10 inches in diameter. The coefficient of friction is 0.01. The turbine makes 250 revolutions per minute.    .
13.   In the preceding problem suppose the shaft which carries the rotating system to be hollow, with an inner diameter of 6 inches and outer diameter of 12 inches.
14.   In problem 12 suppose the bearing to be a hemispherical pivot with constant normal pressure.
15.   In the preceding problem suppose the vertical component of the normal pressure to be constant.